US20150137818A1 - Methods of transient em data compression - Google Patents

Abstract

A system and method to compress transient signals are described. The system includes a transmitter disposed in a borehole to change a transmitted current and induce a current in an earth formation, and a receiver disposed in the borehole to receive the transient signals resulting from the transmitted current. The system also includes a processor to compress the transient signals, the processor compressing the transient signals based on a spline approximation method or an Eigen value method for each transient signal based on whether the spline approximation method or the Eigen value method results in a fewer number of parameters representing the transient signal.

Description

CROSS-REFERENCE TO RELATED APPLICATION
• This application claims the benefit of priority to PCT Application No. PCT/RU2013/001030 filed Nov. 18, 2013, the disclosure of which is incorporated herein by reference in its entirety.
BACKGROUND
• In downhole exploration and production operations, sensors and measurement devices are used to obtain information about a variety of parameters that may be helpful in improving aspects of the efforts. Information about the downhole environment (e.g., pressure, temperature) as well as formations (e.g, resistivity, density) are obtained and processed. The transmission of all of the data obtained downhole for processing at the surface can present challenges when real time processing is desired.
SUMMARY
• According to an aspect of the invention, a system to compress transient signals includes a transmitter disposed in a borehole and configured to change a transmitted current and induce a current in an earth formation; a receiver disposed in the borehole and configured to receive the transient signals resulting from the transmitted current; and a processor configured to compress the transient signals, the processor configured to compress the transient signals based on a spline approximation method or an Eigen value method for each transient signal based on whether the spline approximation method or the Eigen value method results in a fewer number of parameters representing the transient signal.
• According to another aspect of the invention, a method of compressing transient signals includes obtaining the transient signals; compressing, using a processor, the transient signals, the processor compressing each transient signal based on a spline approximation method or an Eigen value method based on whether the spline approximation method or the Eigen value method results in a fewer number of parameters representing the transient signal; and transmitting the parameters representing each transient signal for recovery of the transient signal.
BRIEF DESCRIPTION OF THE DRAWINGS
• Referring now to the drawings wherein like elements are numbered alike in the several Figures:
• FIG. 1 is a cross-sectional view of a system to obtain and compress transient electromagnetic signals according to an embodiment of the invention;
• FIG. 2 is a process flow of a method of compression that includes generating a spline approximation of a TEM signal according to an embodiment of the invention;
• FIG. 3 is a process flow of a method of compression that includes generating Eigen values from a TEM signal according to another embodiment of the invention;
• FIG. 4 shows a portion of the downhole tool in an exemplary case;
• FIG. 5 is a histogram showing exemplary results obtained using 3-14 parameters for XX and YY components of exemplary TEM signals;
• FIG. 6 is a histogram showing exemplary results obtained using 5-20 parameters for XY and YX components of exemplary TEM signals;
• FIG. 7 is a histogram showing exemplary results obtained using 5-20 parameters for XZ and YZ components of exemplary TEM signals;
• FIG. 8 is a histogram showing exemplary results obtained using 4-20 parameters for ZX and ZY components of exemplary TEM signals;
• FIG. 9 is a histogram showing exemplary results obtained using 4-20 parameters for the ZZ component of exemplary TEM signals;
• FIG. 10 illustrates one exemplary TEM signal;
• FIG. 11 illustrates another exemplary TEM signal;
• FIGS. 12 and 13 illustrate exemplary dependence on accuracy of the reconstruction on an average number of parameters of the compressed signal; and
• FIGS. 14 and 15 illustrate recovery error during reconstruction of a compressed signal.
DETAILED DESCRIPTION
• As noted above, real time transmission of data obtained downhole can be challenging because of the volume of data and the available bandwidths for transmission. As such, compression methods for data have been used to reduce the transmitted data set. Embodiments of the system and method described herein relate to transient electromagnetic data compression.
• FIG. 1 is a cross-sectional view of a system to obtain and compress transient electromagnetic signals according to an embodiment of the invention. While the system may operate in any subsurface environment,FIG. 1 shows adownhole tool10 disposed in aborehole2 penetrating theearth3. Thedownhole tool10 is disposed in theborehole2 at a distal end of acarrier5. Thedownhole tool10 may includemeasurement tools11 anddownhole electronics9 configured to perform one or more types of measurements in an embodiment known as Logging-While-Drilling (LWD) or Measurement-While-Drilling (MWD). According to the LWD/MWD embodiment, thecarrier5 is a drill string. The measurements may include measurements related to drill string operation, for example. Adrilling rig8 is configured to conduct drilling operations such as rotating the drill string and, thus, thedrill bit7. Thedrilling rig8 also pumps drilling fluid through the drill string in order to lubricate thedrill bit7 and flush cuttings from theborehole2. Raw data and/or information processed by thedownhole electronics9 may be telemetered to the surface for additional processing or display by acomputing system12. Drilling control signals may be generated by thecomputing system12 and conveyed downhole or may be generated within thedownhole electronics9 or by a combination of the two according to embodiments of the invention. Thedownhole electronics9 and thecomputing system12 may each include one or more processors and one or more memory devices. In alternate embodiments, thecarrier5 may be an armored wireline used in wireline logging. Different layers of the downhole environment may have different resistivities (e.g.,resistivity2 of formation is different than resistivity1) as shown inFIG. 1. Thedownhole tool10 according to embodiments obtains electromagnetic information. Thedownhole tool10 may include one or more transmitters (transmitter coils) that turn the current impulse in the transmitter coil on and off to induce a current in the earth3 (formation4) and one or more receivers that receive the resulting transient electromagnetic (TEM) signals. The transmitter and receiver may be one-, two-, or tri-axis devices, but a tri-axis transmitter and receiver are discussed in the examples below.
• Different embodiments for compressing these TEM signals are detailed below. In each embodiment, the time interval and discrete time points at which a TEM signal is recorded are assumed to be fixed. As such, the time points need not be transmitted along with the TEM signal. The measured time-dependent TEM signals may be preprocessed (e.g., filtered to remove random noise). Transient signals depending on time may be classified based on being: monotonous, non-monotonous like-sign, and non-monotonous and crossing zero at one, two, or three points. A common feature of all TEM signals is that the signals decay as power functions. As further discussed below, different embodiments of the invention may be better-suited to different TEM signals.
• FIG. 2 is a process flow of a method of compression that includes generating a spline approximation of a TEM signal according to an embodiment of the invention. The transformation does not change the sign of the original TEM signal and includes multiplying the TEM signal by power. If the transformation changed the sign (e.g., logarithm or power function of absolute signal value) then the singularity appears in zero and requires additional parameters to describe the signal because auxiliary conditions would have to be included at zero. Atblock210, acquiring the TEM signal includes the transmitter coil of thedownhole tool10 inducing current in the formation and the receiver receiving the TEM signal. The filtering and transforming of the TEM signal atblock220 may be performed by thedownhole electronics9, for example. The transformation is given by:
• 
  F_j=F(t_j),j=1,n,  [EQ. 1]
• where n is the number of time values and is calculated after preprocessing of the recorded TEM signal.
• Atblock230, choosing nodes among discrete time points is based on the type of spline approximation used. As one example, when a cubic spline is used, choosing nodes includes calculating time derivatives at the first and last time points
• $\frac{\partial F}{\partial t}\left(t_1\right),\frac{\partial F}{\partial t}\left(t_n\right),$
• which involves a numerical calculation. The time interval [t₁,t_n] is divided into m−1 intervals, m=2, M, where M is a threshold. When the times grow geometrically, and n (times values) is much bigger than m (number of nodes), then the nodes u_i, i=1,m are determined as
• $\begin{array}{cc}{u}_i=t_j,j=\frac{n}{m-1}·\left(i-1\right)+1,i=1,m-1;u_m=t_n& \left[\mathrm{EQ}.2\right]\end{array}$
• Atblock240, calculating spline coefficients is for the chosen nodes m. In the exemplary case of the cubic spline, calculating spline coefficients is done using the derivatives. Atblock250, recovering the signal transformation includes recovering R_j=R(t_j), j=1,n with the calculated coefficients. Atblock260, comparing the recovered signal with the original signal transformation includes determining a misfit measure Δ as:
• $\begin{array}{cc}\Delta =\sqrt{\frac{1}{n}\sum _{j=1}^n{\left(\frac{F_j-R_j}{F_j·w_j}\right)}^2}·100\%& \left[\mathrm{EQ}.3\right]\end{array}$
• where w_jare the weights.
• Atblock270, determining whether there is a good fit includes determining if the misfit measure Δ is below a predetermined value. When the recovered signal is a good fit with the original transformation, then the process includes providing the results atblock280 as k=m+j parameters, wherein m values of the signal at m nodes and j additional parameters are provided based on the type of spline approximation used. For the exemplary C²(twice continuously differentiable) cubic spline type, 2 additional parameters—the derivatives at the first and last time points—are used. When the recovered signal is not a good fit with the original transformation, then the process includes increasing the number of nodes, m, atblock290, and the spline coefficients are calculated again (block240). This process of assessing the fit continues untilblock280 is reached. After transmission (for example to thecomputing system12 at the surface) to obtain and process the TEM signal, the processor of thecomputing system12 would implement the processing of250.
• FIG. 3 is a process flow of a method of compression that includes generating Eigen values from a TEM signal according to another embodiment of the invention. Atblock310, acquiring the TEM signal includes the transmitter coil of thedownhole tool10 inducing current in the formation and the receiver receiving the TEM signal. The filtering and transforming of the TEM signal atblock320 may be performed by thedownhole electronics9, for example. The TEM signal transformation is given by EQ. 1 and is performed after preprocessing (e.g., filtering) the recorded TEM signal. According to this embodiment, a class of models is chosen for inversion of the TEM signals. The class may include cylindrically-layered, horizontally-layered, or a more complicated medium. Atblock330, selecting the class of models includes selecting the specific class based on the processing intended to be performed with the recovered TEM signal. The number of models used must be greater than the number of time points at which the TEM signal is recorded. As a result, “signal space,” which is an n-dimensional vector space, is obtained, where n is the number of time points. Any measured TEM signal is assumed to belong to this space and, therefore, it is assumed that any measured TEM signal can be represented as a linear combination of the calculated signals. Thus, after choosing the model class (block330), calculations of the synthetic signals for a wide range of medium parameters (e.g., resistivities, distances to bed), that is, calculating basic Eigen vectors, must be performed atblock340. The synthetic signals are given by:
• 
  S_ij=S_i(t_j), i=1,l,j=1,n  [EQ. 4]
• l is the number of obtained models, and n is the number of time points.
  The basic Eigen vectors or orthogonal basis {circumflex over (V)} may be constructed for each vector space. An arbitrary signal from the space may be represented as a linear combination of the basic vectors. The number of terms in the linear representation depends on the required accuracy of the representation. The basic Eigen vectors (orthogonal basis {circumflex over (V)}) are constructed for the matrix Ŝ by a singular value decomposition (SVD) method:
• 
  Ŝ^TŜ·{circumflex over (V)}={circumflex over (V)}·{circumflex over (Λ)}  [EQ. 5]
• where {circumflex over (Λ)} is a diagonal matrix of basic Eigen values. If {circumflex over (Λ)}̂ includes zero Eigen values, then Nr—rank of matrix Ŝ—equals the number of non-zero basic Eigen values. The number of Eigen values m describing the signal cannot be greater than Nr.
• Atblock350, calculating the coefficients of linear representation using k Eigen vectors includes determining the Eigen values {right arrow over (X)} for reconstruction of {right arrow over (F)} as:
• 
  {right arrow over (X)}={circumflex over (V)}·{circumflex over (M)}⁻¹·{right arrow over (F)}  [EQ. 6]
• where {circumflex over (M)}²={circumflex over (Λ)}. On the first step, the signal may be calculated with one basic Eigen vector that corresponds to a maximal basic Eigen value such that {circumflex over (M)} contains only one maximal basic Eigen value and its dimension is 1. The dimension of {right arrow over (X)} is also 1. Atblock360, recovering the signal R_j=R(t_j), j=1,n is based on the calculated Eigen values {right arrow over (X)} according to:
• 
  {right arrow over (R)}{circumflex over (M)}·{circumflex over (V)}^T·{right arrow over (X)}  [EQ. 7]
• Atblock370, comparing the recovered signal with the original signal transformation includes determining a misfit measure A according to EQ. 3. Atblock390, determining whether there is a good fit includes determining if the misfit measure Δ is below a predetermined value. When the recovered signal is a good fit with the original transformation, then the process includes providing the results atblock390 as Eigen values ({right arrow over (X)}). When the recovered signal is not a good fit with the original transformation, then the process includes increasing the number of vectors, atblock355, and the coefficients of linear representation are calculated again (block350). This process of assessing the fit continues untilblock390 is reached. After transmission (for example to thecomputing system12 at the surface) to obtain and process the TEM signal, the processor of thecomputing system12 would implement the processing ofblock350. The number of transmitter parameters (k) is equal to the dimension of the vector {right arrow over (X)}.
• A given TEM signal may be better suited for the method discussed with reference toFIG. 2 or toFIG. 3. Thus, both may be performed and the one resulting in the fewest transmission parameters may be chosen. The structure of the parameters allows a receiving processor to recognize which of the methods was used.
• FIG. 4 shows a portion of thedownhole tool10 in an exemplary case. The exemplary case illustrates the methods discussed above. The spacing between the transmitter (T) and receiver (R) in the exemplary arrangement shown inFIG. 4 is 5 meters (m). When the current impulse in the transmitter coil is turned off, the coil moment is 1 A−m². The electromagnetic field is measured for all components (axial arrangements of the transmitter and receiver: xx, xy, xz, yx, yy, yz, zx, zy, zz). In the example, 200 time points are used from 5 micro seconds to 0.5 milliseconds. The three resistivities (Rt₁, Rt₂, Rt₃) indicated inFIG. 4 may be different values between 1 Ohm-m and 100 Ohm-m. The distance to bed center (D2C) may be a value from 0 to 32 m, and the dip θ and rotation angle φ of thedownhole tool10 may be between 0 and 90 degrees. The signal sets calculated on these models coincide for xx and yy components (78400 models), xy and yx components (57600 models), xz and yz components (67200 models), and zx and zy components (67200 models). For the zz component, 11200 models are computed.
• The signal decays on average as l/t₂on a chosen time interval. Thus, the TEM signal transformation is given by:
• 
  F_j=G(t_j)·t², j=1,n, n=200  [EQ. 8]
• where G(t_j) is the recorded and filtered exemplary TEM signal. The misfit measure Δ (given by EQ. 3 above) is considered acceptable if Δ is less than or equal to 0.5%. The weights w_jare determined by initially setting w_jas 1, j=1,n then increasing the weights near zero. If F_i−1·F_i<0 then
• $w_{i-2}=\frac{F_{i-3}}{F_{i-2}},w_{i-1}=\frac{F_{i-3}}{F_{i-1}},w_i=\frac{F_{i+2}}{F_i},w_{i+1}=\frac{F_{i+2}}{F_{i+1}}.$
• Calculations of signal transformation are obtained for the above models.
• According to one exemplary illustration, the Eigen value method described with reference toFIG. 3 is used. An additional model set is needed to construct the orthogonal basis {circumflex over (V)}. The first set of models for calculation of the synthetic signals and the additional model set are disjoint. The range of parameters for the second set is smaller. Thus, the orthogonal basis {circumflex over (V)} is constructed for the different signals that are recovered for the same class of models. A class of 3-layer models may be enough for the description of the TEM signals in the layered medium with an arbitrary number of the boundaries. Several experiments using the Eigen values method described with reference toFIG. 3 above show that the signals calculated for 4-, 5-, and 6-layer models are recovered with the same number of parameters as the ones calculated for the initial 3-layer model.
• FIGS. 5-9 are histograms indicating the percentage of TEM signals that can be decompressed as a function of the number of parameters. Thex axis510 shows the number of parameters and they axis520 shows the corresponding percentage of TEM signals that can be decompressed. For the spline approximation method, the C²cubic spline type was used. Using the exemplary spline type, the minimal number of parameters is 4, namely the signal transformations and their derivatives at the first and last time points. None of the exemplary TEM signals requires more than 23 parameters for recovery. The average number of parameters needed for the exemplary TEM signals is between 6.3 and 10.8. It was found that 200 values of TEM signals represent strongly redundant data. The average number of parameters is given by:
• $\begin{array}{cc}{N}_{\mathrm{average}}=\frac{\sum _{i=1}^{23}i·q_i}{\sum _{i=1}^{23}q_i}& \left[\mathrm{EQ}.9\right]\end{array}$
• where q_iis the number of signals which can be recovered with i parameters.
• FIG. 5 is a histogram showing exemplary results obtained using 3-14 parameters for XX and YY components of exemplary TEM signals. AsFIG. 5 indicates, the average number of parameters required using the spline approximation method discussed with reference toFIG. 2 is 7.7. The average number of parameters required using the Eigen value method discussed with reference toFIG. 3 is 7.2, and the average number of parameters required using the combination method—which tests both approaches and selects the one, for each given TEM signal, requiring the lowest number of parameters—is 6.8 parameters. The spline approximation method uses fewer parameters (relative to the Eigen value method and the combination method for 26% of the TEM signals. The Eigen value method uses fewer parameters (relative to the spline method and the combination method) for 52% of the TEM signals. The spline method and the Eigen value method both use the same number of parameters for 22% of the TEM signals.
• FIG. 6 is a histogram showing exemplary results obtained using 5-20 parameters for XY and YX components of exemplary TEM signals. AsFIG. 6 indicates, the average number of parameters required using the spline approximation method is 10.8. The average number of parameters required using the Eigen value method is 9.6, and the average number of parameters required using the combination method is 9.18 parameters. The spline approximation method uses fewer parameters (relative to the Eigen value method and the combination method) for 26% of the TEM signals. The Eigen value method uses fewer parameters (relative to the spline method and the combination method) for 61% of the TEM signals. The spline method and the Eigen value method both use the same number of parameters for 13% of the TEM signals.
• FIG. 7 is a histogram showing exemplary results obtained using 5-20 parameters for XZ and YZ components of exemplary TEM signals. AsFIG. 7 indicates, the average number of parameters required using the spline approximation method is 10.3. The average number of parameters required using the Eigen value method is 9.2, and the average number of parameters required using the combination method is 8.7 parameters. The spline approximation method uses fewer parameters (relative to the Eigen value method and the combination method) for 25% of the TEM signals. The Eigen value method uses fewer parameters (relative to the spline method and the combination method) for 59% of the TEM signals. The spline method and the Eigen value method both use the same number of parameters for 16% of the TEM signals.
• FIG. 8 is a histogram showing exemplary results obtained using 4-20 parameters for ZX and ZY components of exemplary TEM signals. As FIG. 8 indicates, the average number of parameters required using the spline approximation method is 10.7. The average number of parameters required using the Eigen value method is 9.7, and the average number of parameters required using the combination method is 9.1 parameters. The spline approximation method uses fewer parameters (relative to the Eigen value method and the combination method) for 30% of the TEM signals. The Eigen value method uses fewer parameters (relative to the spline method and the combination method) for 58% of the TEM signals. The spline method and the Eigen value method both use the same number of parameters for 12% of the TEM signals.
• FIG. 9 is a histogram showing exemplary results obtained using 4-20 parameters for the ZZ component of exemplary TEM signals. As FIG. 9 indicates, the average number of parameters required using the spline approximation method is 7.1. The average number of parameters required using the Eigen value method is 6.7, and the average number of parameters required using the combination method is 6.3 parameters. The spline approximation method uses fewer parameters (relative to the Eigen value method and the combination method) for 30% of the TEM signals. The Eigen value method uses fewer parameters (relative to the spline method and the combination method) for 48% of the TEM signals. The spline method and the Eigen value method both use the same number of parameters for 22% of the TEM signals.
• As the examples above illustrate, the combination method (selecting by comparing the results of the spline method and the Eigen value method) does not significantly decrease the average number of parameters that must be transmitted to recover the original TEM signal. This indicates that there are no special classes of curves (TEM signals) for which one of the methods of data compression is preferable (results in fewer required numbers of parameters).
• FIG. 10 illustrates one exemplary TEM signal. The ZZ component is shown inFIG. 10. Time is shown on thex axis1010, and voltage based on the measured TEM signal is shown on they axis1020. The exemplary curve is obtained with a setup shown inFIG. 4 having resistivity values: Rt₁=3.16 Ohm-m; Rt₂=1 Ohm-m; Rt₃=100 Ohm-m, height of the layer (H)=0.5 m, D2C=0 m, tool dip angle (θ)=60 degrees, and rotation angle (φ)=0 degrees. The curve shown inFIG. 10 may be represented by 3 parameters based on the Eigen values method and 4 parameters based on the spline approximation method.
• FIG. 11 illustrates another exemplary TEM signal. The XZ component is shown inFIG. 11. Time is shown on thex axis1010, and voltage based on the measured TEM signal is shown on they axis1020. The exemplary curve is obtained with a setup shown inFIG. 4 having resistivity values: Rt₁=1 Ohm-m; Rt₂=31.6 Ohm-m; Rt₃=10 Ohm-m, height of the layer (H)=15 m, D2C=24 m, tool dip angle (θ)=45 degrees, and rotation angle (φ)=0 degrees. The curve shown inFIG. 11 may be represented by 19 parameters based on the Eigen values method and 14 parameters based on the spline approximation method.
• FIGS. 12 and 13 illustrate exemplary dependence on accuracy of the reconstruction on an average number of parameters of the compressed signal. Accuracy is shown on thex axis1210, and the average number of parameters are shown on they axis1220 for the Spline approximation method (FIG. 12) and for the Eigen values method (FIG. 13).
• FIGS. 14 and 15 illustrate recovery error during reconstruction of a compressed signal. Time in seconds is shown on thex axis1410, and recovery error as a percentage (%) is shown on the y axis1420 for the Spline approximation method (FIG. 14) and for the Eigen values method (FIG. 15). AsFIG. 14 illustrates, the recovery error related to the Spline approximation method looks sinusoidal. The recovery error is zero in 6 spline nodes and is either maximal or indicates a change in sign in the center of the interval between nodes. The recovery error resulting from using the Eigen values method also shows some regularity. The recovery looks cosinusoidal.FIG. 15 indicates 7 intervals and 2 semi-intervals with similar error behavior. The number of whole intervals equals the number of decompression parameters. The error at a given point in time may be considered as a random variable. Then, the distribution of the random variable may be studied and used in the inversion scheme.
• While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation.

Claims (20)

1. A system to compress transient signals, the system comprising:

a transmitter disposed in a borehole and configured to change a transmitted current and induce a current in an earth formation;

a receiver disposed in the borehole and configured to receive the transient signals resulting from the transmitted current; and

a processor configured to compress the transient signals, the processor configured to compress the transient signals based on a spline approximation method or an Eigen value method for each transient signal based on whether the spline approximation method or the Eigen value method results in a fewer number of parameters representing the transient signal.

2. The system according toclaim 1, further comprising a telemetry system to transmit the parameters representing the transient signal to a surface processor.

3. The system according toclaim 1, wherein the processor is disposed in the borehole and transmits the parameters representing each transient signal to a surface location.

4. The system according toclaim 1, wherein the processor performs filtering and a transform of each transient signal prior to compression.

5. The system according toclaim 1, wherein the processor is configured to implement the spline approximation method by selecting a spline type.

6. The system according toclaim 5, wherein the processor is further configured to calculate spline coefficients as the parameters representing the transient signal for each transient signal based on choosing nodes among discrete time points according to the spline type.

7. The system according toclaim 6, wherein the processor iteratively calculates the spline coefficients based on a comparison of a signal recovered from the spline coefficients with the transient signal represented by the spline coefficients.

8. The system according toclaim 1, wherein the processor is configured to implement the Eigen value method by calculating basic Eigen vectors based on selecting a class of models.

9. The system according toclaim 8, wherein the processor is further configured to calculate coefficients of linear representation of the transient signal as the parameters representing the transient signal using the basic Eigen vectors.

10. The system according toclaim 9, wherein the processor selects the class of models based on a type of processing expected for the transient signal recovered from the coefficients.

11. A method of compressing transient signals, the method comprising:

obtaining the transient signals;

compressing, using a processor, the transient signals, the processor compressing each transient signal based on a spline approximation method or an Eigen value method based on whether the spline approximation method or the Eigen value method results in a fewer number of parameters representing the transient signal; and

transmitting the parameters representing each transient signal for recovery of the transient signal.

12. The system according toclaim 11, wherein the obtaining the transient signal includes disposing a transmitter in a borehole, the transmitter configured to change a current transmitted into a formation, and disposing a receiver in the borehole, the receiver configured to receive the transient signals based on current induced in the formation by the transmitter.

13. The method according toclaim 11, further comprising filtering and transforming each transient signal prior to the processor compressing the transient signals.

14. The method according toclaim 13, wherein the transforming each transient signal is based on a number of time values at which the transient signal is recorded.

15. The method according toclaim 11, wherein the processor compressing the transient signal based on the spline approximation method includes selecting a cubic spline type and calculating time derivatives at a first time point and a last time point at which the transient signal is recorded.

16. The method according toclaim 15, wherein the processor compressing the transient signal based on the spline approximation method further includes calculating spline coefficients as the parameters representing the transient signal based on values of the transient signal at selected nodes and on the time derivatives calculated for the transient signal.

17. The method according toclaim 16, further comprising the processor iteratively calculating the spline coefficients based on a comparison of a signal recovered from the spline coefficients with the transient signal represented by the spline coefficients.

18. The method according toclaim 11, wherein the processor compressing the transient signal based on the Eigen value method includes calculating basic Eigen vectors based on selecting a class of models.

19. The method according toclaim 18, wherein the processor compressing the transient signal based on the Eigen value method further includes calculating coefficients of linear representation of the transient signal as the parameters representing the transient signal using the basing Eigen vectors.

20. The method according toclaim 19, further comprising the selecting the class of models based on a type of processing expected for the transient signal recovered from the coefficients.

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